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Bitcoin may finally be on its way toward legitimacy this year, what with Overstock.com accepting it for payments and bitcoin ATMs popping up. But the most intriguing parts of bitcoin -- and all its cousin currencies like litecoin, peercoin, and even dogecoin -- are the core mathematical algorithms that power it.

Now those algorithms are appearing in contexts that hint at how cryptocurrency is only one possible application for such math, and how other applications may be even more powerful and socially useful.

First, some background: Blockchain technology -- the core math used in bitcoin, as explained by its creator -- is a way to decentralize items that weren't previously considered decentralizable. Paul Bohm's explanation, in a Quora post, describes it as "a means to make consensus in highly distributed large-scale systems, which would otherwise never be able to reach consensus. The value of this is, that it's now possible to build applications in a decentralized fashion, that we previously thought could not be built without a central authority."

The larger question of what kinds of applications is now getting much more attention. Consider Twister, a microblogging/social networking application that borrows technology from both bitcoin and BitTorrent. Twister runs on no central server but rather on an aggregate of individual, peer-to-peer clients. A blockchain that runs between clients verifies that user accounts are unique and posts from a given account really belong to that account. A similar project, Bitmessage, is for simple peer-to-peer messaging and might even function as a secure replacement for email depending on the implementation.

Another application of the bitcoin network was discussed by Jeremy Clark of Carleton University and Aleksander Essex of the University of Waterloo, who proposed using the bitcoin system itself as a way to verify the timestamp of a given action, what they call "carbon dating." Such a technique could be used for verifiable electronic voting, with the bitcoin blockchain making forgery nearly impossible.

These projects also show two major ways bitcoin's technology can be reused. The first one involves using the same protocol as bitcoin, but not the currency's actual network. The second approach uses bitcoin's protocol and network -- in essence, leveraging the existing presence of the network to distribute the data.

Again, the breadth of applications -- and some potential pitfalls -- are only just now beginning to become clear. Namecoin, for instance, uses its own bitcoin-style blockchain to create a secure domain name system as a possible alternative to the standard ICANN domain registry. A great idea, but it didn't stop cyber squatters from snapping up domains cheaply and then trying to resell them for a profit.

Most of the current hubbub around bitcoin revolves around its use as a currency -- the value of a bitcoin versus the dollar, and whether or not governments will accept its legitimacy. But the underlying math has a power and utility that outstrips any of bitcoin's financial implications. It'll be fascinating to see how those develop, entirely apart from and in parallel with the cryptocurrency itself.